I think 2 because the expression of 2 can be simplified as --> there exist(S(x)) ∧ ~V(x))
where as 1 states--> ~ (if a logic is satisfiable then it is valid)..this means if a logic is satisfiable then it is not valid..but this is not the case, it may be valid may not be valid
Not = ~
Every = $\forall$
logic = $x$
Satisfiable = $S( )$
Valid = $V()$
“Not every satisfiable logic is valid” ( It means that the underline statement is not true)
= Not (every satisfiable logic is valid)
=Not( For all logic if a logic is satisfiable then it will be valid)
= $\sim ( \forall(x) S(x) \rightarrow V(x) )$
why "if....then"??
"is" represents by $"\rightarrow" ??$
"is"
if I say like this
"every logic satisfiable AND valid"
AND
then where is error?
"every logic satisfiable AND valid" will not hold.
Because valid is depending on satisfiable.
AND means no dependency.
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